I'm still a beginner and bought a used set (Vintage V-100 and Roland Cube 15x).
The guitar is not bad but will be replaced when I get better (I like Mayones), but at this point it is OK but this small Roland amp is driving me crazy.
I don't get a good sound out of it and it is a pain to remember the settings which were more or less OK.

So before going to tube amps (I need to discover my preferences first) I wanted to buy a modelling amp first. I like the sound of the Fender Mustang III and the endless possibilities to experiment.
But, I don't need the power (100w) as the 15w I have now are already plenty and the effects are built in.

My question, would it be a good idea to buy an effect generator like the Boss/Roland GT-10 (or comparable) instead of the Mustang?
Like the Mustang it provides several amps settings with the distinctive sounds/tones and even a multitude more effects which are portable (can be connected to any amp).
Which is the most important factor that gives the Mustang the good sound qualities/tones? The built-in generator or the amp itself? Probably a combination but the generator must be the primary factor.
Would a GT-10 in combination with my small practice amp give me a comparable sound?
Just because I have some strong opinions doesn't mean I agree with everything I say.
I used to have the Boss GT-10. It's great, but useless with a 15 W modeling amp. I think you should upgrade your amp first and then buy the GT-10, but don't get a modeling amp: the GT-10 has everything you need, including amp simulation.
It's up to you. The nice thing about a multifx is that you can change amps without losing your FX box. Since you are a beginner I'd advise you to consider something with a drum machine. It's an extremely important practice tool and can actually make you sound better. You could continue to use your 15x on a clean setting or the aux input, and look for a godo deal on a tube amp.

The Digitech RP355 is a good value and has a drum machine.
I would stay away from modeling amps. fly135 had a great suggestion about the drum machine. I bought a used Digitech GNX3 multi fx pedal (which also does modeling but I stay away from those features) and love it (I was considering the RP355 but found a deal on a GNX3).